Run chart interpretation in quality improvement studies

In general, the heuristics used by the statistical process control engineers are reasonable if you are using materials developed by Donald Wheeler, W. Edwards Deming, or the grandfather of these methods – Walter Shewhart.

But my question: Is there an error in the text for rule one that describes a shift? If I did the math right, a binary event with a probability of 0.5 that occurs exactly 6 consecutive times is \frac{1}{2^6} = 0.015625, for 7, it is \frac{1}{2^{7}} = 0.0078125 neither of which I consider close enough to “less than 3 in 1000”.

A long time ago, I wrote a program to explore the relationship among various measures of information described in the link below; the numbers in the quoted text looked wrong to me. Is there a more charitable interpretation, or did the authors simply get the computations wrong?

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